This distribution extend the lambda second distribution introduced in c22b;textualCohensdpLibrary as the exact solution to the predictive distribution of the Cohen's dp in repeated-measure when the population correlation is known. A more elegant notation was provided in l22;textualCohensdpLibrary. The prior-informed lambda prime is a bayesian extension to the lambda prime distribution in the case where the population rho is not known. It is then replaced by a prior which indicates the probability of a certain rho given the observed correlation r.
ppilsecond(delta, n, d, r)
dpilsecond(delta, n, d, r)
qpilsecond(p, n, d, r)
pilsecond are (p,d,q) functions that compute the prior-informed Lambda-second (L") distribution. This distribution is an generalization of the lambda-prime distribution l99CohensdpLibrary. It can take up to two seconds to compute.
Note: the parameters are the raw sample size n, the observed Cohen's dp, and the sample correlation r. All the scaling required are performed within the functions (and so you do not provide degrees of freedom). This is henceforth not a generic lambda-second distribution, but a lambda-second custom-tailored for the problem of standardized mean difference.
### Note: this distribution can be slow to compute
### dpilsecond(0.25, 9, 0.26, 0.333) # 1.186735
### ppilsecond(0.25, 9, 0.26, 0.333) # 0.5150561
### qpilsecond(0.01, 9, 0.26, 0.333) # -0.7294266